Journal of Electroanalytical Chemistry 779 (2016) 187–198
Contents lists available at ScienceDirect
Journal of Electroanalytical Chemistry
journal homepage: www.elsevier.com/locate/jelechem
Heterogeneous versus homogeneous electron transfer reactions at
liquid–liquid interfaces: The wrong question?
Pekka Peljo ⁎, Evgeny Smirnov, Hubert.H. Girault
Laboratoire d'Electrochimie Physique et Analytique, École Polytechnique Fédérale de Lausanne, EPFL Valais Wallis, Rue de l'Industrie 17, Case Postale 440, CH-1951 Sion, Switzerland
a r t i c l e
i n f o
Article history:
Received 28 January 2016
Received in revised form 11 February 2016
Accepted 14 February 2016
Available online 18 February 2016
Keywords:
Liquid–liquid interfaces
Electron transfer
Ion transfer
Finite element simulations
Redox catalysis
a b s t r a c t
The exact mechanism of the electron transfer reactions at liquid–liquid interfaces still remains a source of interrogation. The purpose of this paper is to revisit this topic using a finite element simulation approach to analyze
cyclic voltammograms for some previously published systems. Also, we compare the voltammograms obtained
in the absence or presence of an adsorbed gold nanoparticle film. The current results indicate that the electron
transfer between ferrocene in the organic phase and hexacyanoferrate(III) in the aqueous phase takes place by
a potential independent homogeneous reaction in the aqueous phase, while the observed potential dependence
stems from that of the concomitant ion transfer reaction of ferrocenium. In the presence of the interfacial gold
nanofilm the electron transfer takes place by a bipolar mechanism where the electrons are shuttled through
the metallic nanofilm.
© 2016 Elsevier B.V. All rights reserved.
1. Introduction
Since the early days of electrochemistry at liquid–liquid interfaces, it
was quickly realized that it was possible to polarize the interface between two immiscible electrolytes by building up two face-to-face
Gouy–Chapman layers [1,2]. Then, a lot of emphasis was given to ion
transfer reactions. These reactions are fast, potential dependent and by
now rather well understood [2,3]. Following the pioneering work of
Koryta et al. [4–6], assisted ion transfer reactions were investigated
using an ionophore mainly in the organic phase to facilitate the transfer
of aqueous ions.
Then, attention was given to electron transfer reactions between a
donor (D) in one phase and an acceptor (A) in the other phase. Since
the early work of Samec et al. [7–9] and others [10], who had shown
that a current could be measured when ferrocene was used as an organic donor and ferrocyanide as an aqueous acceptor, heterogeneous electron transfer reactions at polarized liquid–liquid interfaces have
remained a source of interrogation. Indeed, the main questions are:
How much of the total interfacial potential drop does the precursor
bD | A N “feel” at the interface? Where does the potential dependence
of the observed current stem from? Do some reactants either D or A partition prior to homogeneous electron transfer reactions, and in this case
is the current measured due to ion transfer reactions of either the
charged reactant or charged product? This problem is actually somewhat analogous to facilitated ion transfer, that can take place according
⁎ Corresponding author.
E-mail address: pekka.peljo@epfl.ch (P. Peljo).
http://dx.doi.org/10.1016/j.jelechem.2016.02.023
1572-6657/© 2016 Elsevier B.V. All rights reserved.
to at least four different mechanisms, and the differentiation of these
mechanisms is very difficult [2,3].
Heterogeneous electron transfer reactions at ITIES are known to be
potential dependent, i.e. dependent of the interfacial polarization but
it is difficult to evaluate how much of the overall polarization is active
as a local driving force. In early days, these reactions were thought to
be truly heterogeneous ET, as suggested by Samec et al. [11,12], for
the system comprising K3/4[Fe(CN)6] in water and ferrocene in the organic phase, meaning that one aqueous redox couple is supposed to
react with an organic redox species only at the interface. Then, it had
been postulated e.g. by Kihara et al. [13], Osakai et al. [14] and Katano
et al. [15,16] that one of the reactants can in fact partition to undergo
a homogenous ET with associated ion transfer reactions and that the
measured current was not always due to a heterogeneous ET but rather
to the preceding or following ion transfer reaction.
Using simple techniques such as cyclic voltammetry did not really
help in resolving the matter. Of course, a methodology to treat heterogeneous electron transfer reactions was developed for example by
Stewart et al. [17], and by Senda et al. for normal pulse voltammetry
[18]. New techniques based on scanning electrochemical microscopy
were then used and for example Mirkin et al. concluded that “The observed change in the ET rate with the interfacial potential drop cannot
be attributed to concentration effects and represents the potential dependence of the apparent rate constant” [19]. However, they later concluded that “the rate constant of ET across the ITIES is essentially
independent of interfacial potential drop when the organic redox reactant is a neutral species” [20]. Similarly, Shi and Anson also reported potential independent ET utilizing thin layer cell voltammetry [21],
188
P. Peljo et al. / Journal of Electroanalytical Chemistry 779 (2016) 187–198
although Unwin et al. later showed that this observation may have been
due to the diffusion limitations [22].
Recently, Aoki et al. have reported, by re-examining the work of Shi and
Anson [21], that the electron transfer reaction may actually take place via a
self-emulsification of aqueous droplets containing the hydrophilic redox
couple into the organic phase. The self-emulsification occurs due to the
mixing entropy even without surfactants [23]. This has been verified experimentally by observing oil droplets in aqueous phase by both voltammetry
and dynamic light scattering [24], and observation of water droplets near
the liquid–liquid interface by optical microscopy [25].
These conflicting results on the potential dependence of the electron
transfer arise from the poor understanding of the potential distribution
within the interfacial layers. The question remains, which mechanism
operates in the electron transfer process at liquid/liquid interfaces? Recently, Li Niu et al. [26] argued (based on the earlier work by Schmickler
[27]) that the potential drop at the interface is mostly at the organic
phase, and hence change of the Galvani potential difference only changes the surface concentrations, leading to a change in the reaction rate.
Samec argued that this assumption is unjustified, as the potential drop
is located at the nanoscopic interface [28]. Girault et al. estimated that
ca. 30% of the potential drop is within the inner layer, so that the electron transfer kinetics depend on the Galvani potential difference and
the diffuse layer effects (Frumkin effect) [29]. X-ray reflectivity and molecular dynamics simulations have indicated that the potential drop is
very sharp: the electron density profile shows a sharp change over
0.2 nm distance [30], and electric potential difference simulated for a
slab of water-DCE-water shows a similar sharp decrease [31]. So far,
X-ray reflectivity and molecular dynamics have not been applied to
study electron transfer reactions, but these techniques would help to
elucidate how the reactions actually happen. Recently, molecular dynamics simulations have been employed to study photoinduced electron transfer between coumarin 314 and N,N-dimethylaniline [32].
Spectroscopic techniques such as surface second harmonic generation [33] and potential modulated fluorescence [29] have also been utilized to study interfacial electron transfer reactions, as well as timeresolved Raman [34]. From all these studies, it is clear that the difficulty
in defining molecularly interfaces makes it difficult in truly defining heterogeneous electron transfer reactions.
The purpose of this paper is to revisit this topic using a finite element
simulation approach to analyze cyclic voltammograms for some previously published systems. Also, we compare the voltammograms obtained in the absence and presence of an adsorbed gold nanoparticle film,
because addition of the gold nanofilm changes the reaction mechanism
to purely heterogeneous interfacial electron transfer, where the electrons are shuttled through the gold nanoparticles, allowing more accurate determination of formal potentials of the organic redox couple.
2. Material and methods
2.1. Chemicals
All chemicals were used as received without further purification. All
aqueous solutions were prepared with ultrapure water (Millipore MilliQ, specific resistivity 18.2 MΩ·cm). Bis(triphenylphosphoranylidene)ammonium chloride (BACl 98%), tetramethylammonium
chloride (TMACl 98%), tetrapropylammonium chloride (TPropACl
98%), lithium chloride (LiCl N99%), lithium sulfate (Li2SO4 N 99%),
Dichlorodimethylsilane (DCDMS) and Ferrocene (Fc) were purchased
from Fluka. α,α,α-Trifluorotoluene (TFT 99% +) was purchased from
Acros. K3Fe(CN)6 (99% +) was obtained from Sigma-Aldrich and
K4Fe(CN)6 (p.a.) from AppliChem. Bis-(triphyenlylphosphoranylidene)
ammonium tetrakis-(pentafluorophenyl)borate (BATB) was prepared
by metathesis of aqueous equimolar solutions of BACl and lithium
tetrakis(pentafluorophenyl)-borate ethyl etherate (LiTB purum, Boulder Scientific). The resulting precipitates were filtered, washed, and recrystallized from an acetone:methanol (1:1) mixture.
38 nm diameter gold nanoparticles (AuNPs) were synthesized by seedmediated growth and used for functionalization of the liquid–liquid interface with a gold nanofilm as reported earlier [35]. Detailed characterization
of the particles and the nanofilm has been reported in ref. [35].
2.2. Electrochemical measurements
All ITIES voltammetry measurements at the water-TFT interface
were performed using a four-electrode cell following the configuration
described previously by Hatay et al. [36] and illustrated in Scheme 1. CVs
of electron transfer between Fc in the organic phase and a mixture of
[Fe(CN)6]3−/4– in the aqueous phase were recorded, with the ratio between [Fe(CN)6]3− and [Fe(CN)6]4− selected as described in Scheme
1A. Low concentrations of Fc (0.1 to 0.5 mM) were used in order to
avoid the presence of Fc+ peak on CVs, which normally exists at ambient conditions with oxygen [37,38]. The set of experiments was carried
out with either 100 mM LiCl (Scheme 1A) or 10 mM Li2SO4 (Scheme 1B)
as supporting electrolyte. Additional experiments were performed with
lower [Fe(CN)6]3−/4– concentrations, at different scan rates.
Two platinum electrodes provide current whereas two Ag/AgCl reference electrodes allow measurement and correction of the polarization
across the interface with PGSTAT 30 and PGSTAT 101 (Metrohm,
Switzerland) potentiostats. Ag/AgCl reference electrode gave a stable
potential also in Cells 4–7. The Galvani potential difference, in accordance with the TATB assumption [39], was calibrated by addition of internal standards TMA+ and TProA+ ions, whose Δw
o ϕ1/2 at the waterTFT interfaces were taken to be + 0.270 V and − 0.019 V for TMA+
and TProA+, respectively [40–42].
3. Theory
Generally the electron transfer reaction between electron-donor D
in the organic phase and an electron acceptor A in the aqueous phase
proceeds by formation of a b D|AN intermediate at the transition state.
To consider the questions posed in the introduction, namely: i) How
much of the total interfacial potential drop does the precursor b D|AN
“feel” at the interface? ii) Where does the potential dependence of the
observed current stem?, finite element simulations of different possible
scenarios were performed. The possible pathways are
k f1
k f2
DðoÞ þ AðwÞ ⇄ bDANðoÞ ⇄ Dþ ðoÞ þ A− ðwÞ
ð1Þ
k f1
k f2
DðoÞ þ AðwÞ ⇄ bDANðinterfaceÞ ⇄ Dþ ðoÞ þ A− ðwÞ
ð2Þ
k f1
k f2
DðoÞ þ AðwÞ ⇄ bDANðwÞ ⇄ Dþ ðoÞ þ A− ðwÞ
ð3Þ
kb1
kb2
kb1
kb1
kb2
kb2
Obviously, reactions (1) and (3) (organic or aqueous pre-partitioning
mechanisms, respectively) require one of the reactants to partition into
the other phase before the reaction. As the transfer of [Fe(CN)6]3− and
[Fe(CN)6]4− into the organic phase requires very negative potentials, reaction (1) is unlikely. Unfortunately, the simulations of the electric double
layer effects are very challenging to implement accurately, so the potential
drop was assumed to occur fully at the liquid–liquid interface. The effect of
the electric double layer was only considered indirectly by varying the
charge transfer coefficient for the interfacial electron transfer in reaction
(2) (heterogeneous electron transfer mechanism). Samec has argued that
low values of α can be reasonable due to the strong repulsion of negatively
charged ferricyanide from the electric double layer on the aqueous side, due
to the Frumkin effect [8,28].
Additionally, Aoki et al. have recently demonstrated that the selfemulsification of the both phases leading to formation of small droplets
of water in the organic phase and small droplets of oil in the aqueous
phase can influence electron transfer reactions at liquid–liquid
P. Peljo et al. / Journal of Electroanalytical Chemistry 779 (2016) 187–198
189
Scheme 1. Composition of four-electrode cells: (A) with 100 mM LiCl and (B) 10 mM Li2SO4 as supporting electrolyte. D denotes electron-donor molecules such as Fc.
interfaces. As some Fc remains in the oil droplets and [Fe(CN)6]3− in the
water droplets, the ET reaction may proceed also “homogenously” within both oil and aqueous phase due to this self-emulsification [43]. However, this mechanism is difficult to implement in the simulations
accurately, so it was not considered in this work.
The model equations used to simulate these voltammograms with
COMSOL Multiphysics v.5.2 are described in the Supplementary material, sections S1 and S2. Following reactions take place at the liquid–liquid
interface:
kET; f
3−
4−
FcðoÞ þ FeðCNÞ6
ðwÞ ⇄ Fcþ ðoÞ þ FeðCNÞ6
ðwÞðheterogeneous ETÞ
The equilibrium constant Khom = k1/k−1 can be evaluated when the
redox potentials of both redox couples are known. [EFc0′+/Fc ]w =
0.381 V vs. SHE [44] and the formal potential for ferro-ferricyanide
0'
3−
4−]
[EFe(CN)
w was evaluated as 0.467 V vs. SHE in 100 mM LiCl
6 /Fe(CN)6
[35] and as 0.4445 V vs. SHE in 10 mM Li2SO4 in this work. The equilibrium constant for the reaction (8) can be calculated as
h
i
h 0
i 0
−ΔG
F
¼ exp
E0FeðCNÞ3− =FeðCNÞ4− − E0Fcþ =Fc
K hom ¼ exp
6
6
w
w
RT
RT
¼ 30:1ðLiClÞ or 12:4ðLi2 SO4 Þ
ð9Þ
kET;b
ð4Þ
kP; f
FcðwÞ ⇄ FcðoÞ ðpartition of ferroceneÞ
kP;b
kIT; f
ð5Þ
Fcþ ðwÞ ⇄ Fcþ ðoÞ ðIT of ferroceniumÞ
ð6Þ
kIT2; f
Kþ ðwÞ ⇄ Kþ ðoÞ IT of Kþ cation
ð7Þ
kIT;b
kIT2;b
where K+ is the metal cation from the ferro-ferricyanide salts. The kinetics of these reactions were assumed to follow a Butler–Volmer formalism, as described in the Supplementary material. As Fc can
partition into the aqueous phase according to Eq. (5), it will react homogeneously with Fe(III):
k1
3−
4−
ðwÞ ⇄ Fcþ ðwÞ þ FeðCNÞ6
ðwÞ
FcðwÞ þ FeðCNÞ6
k−1
ð8Þ
The kinetics for partition of neutral ferrocene were employed by calculating the partition coefficient of Fc, Kp, setting kP,b as 0.1 cm s−1 and
calculating the forward rate constant kP, f = KpkP, b. Partition coefficient
of Fc between TFT and water was calculated from the thermodynamic
cycle as described by Fermin and Lahtinen [45]. Briefly, standard potential of a redox couple in organic solvent can be expressed with the help
as the redox potential in water and the Gibbs energies of transfer of reduced and oxidized species from water to oil:
h
0
E0ox=red
i
o
0;w→o
h 0
i
ΔGox
−ΔG0;w→o
red
¼ E0ox=red þ
w
F
ð10Þ
Hence, the formal potential of Fc in TFT can be expressed as
h
h 0
i
ΔG0;w→o
00
Fc
ð11Þ
¼ E0Fcþ =Fc þ Δw
o ϕFcþ −
o
w
F
This equation can be used to calculate the transfer energy and
also partition coefficient of Fc from water to TFT (standard redox po0'
+
tentials of Fc in water ([EFc
/Fc]w = 0.381 V vs. SHE [44]) and TFT
0'
+
([EFc
]
=
0.736
V
vs.
SHE as obtained in this work, vide infra,
/Fc o
0
E0Fcþ =Fc
i
190
P. Peljo et al. / Journal of Electroanalytical Chemistry 779 (2016) 187–198
Fig. 1. Effect of the standard rate constant on the simulated cyclic voltammograms considering only heterogeneous electron transfer. Experimental and simulated CVs for cell compositions
1 (a) and 3 (b) in Scheme 1 (Fe2+/3+ ratios of 10 to 100 and 100 to 10 respectively) are presented. c) Effect of the homogeneous rate constant on the simulated cyclic voltammograms
considering only homogeneous electron transfer in the aqueous phase, for cell composition 2 in Scheme 1 (Fe2+/3+ ratio of 55 to 55). d) Simulated cyclic voltammograms considering
only partition of ferrocene followed by homogeneous electron transfer and transfer of Fc+ ions across the interface, with three different concentration ratios of Fe2+/3+ in the aqueous
phase. Homogenous reaction rate k1 = 1 × 109 s−1·M−1. Scan rate 10 mV·s−1, only the second scan is shown.
0'
or 0.720 V vs. SHE [35]) are known, and Δw
o ϕ Fc + was taken as the
half-wave potential of Δw
o ϕ1/2 , Fc+ = 0.115 V [35]) as
K p;Fc ¼ exp
ΔG0;w→o
Fc
RT
4.1. Electron transfer across the liquid–liquid interface
!
¼ 13373
ð12Þ
This partition coefficient is similar to the values measured between
water and DCE [45] and water and nitrobenzene [14].
When a gold nanofilm [35] was added at the interface, the system
was considered as a metallic electrode in between the two phases,
where the reactions are only oxidation of Fc at the oil side and reduction
of Fe(III) in the aqueous phase, similarly to bipolar cells [46].
ko;ox
FcðoÞ ⇄ Fcþ ðoÞ þ e−
ð13Þ
kw;ox 4−
3−
ðwÞ ⇄ FeðCNÞ6
ðwÞ þ e−
FeðCNÞ6
ð14Þ
ko;red
kw;red
4. Results and discussion
In this case, simulations were performed in conditions where aqueous redox couple was always in hundred-fold excess. Hence, the Fermi
level of the AuNPs was fixed by the ferro-ferricyanide redox couple
0'
3−
4− ]
(ENP ≈ [EFeCN
w + ϕw), and the overpotential is mostly on the
6 /FeCN6
oil side [35]. For example, the overpotential with the Fe(II)/Fe(III)
ratio of 1/10 in the aqueous phase was only 0.4 mV at the positive potential limit of the scan.
4.1.1. Homogeneous and heterogeneous mechanisms
As discussed above, the electron transfer reaction between Fc in
the TFT phase and Fe(III) in the aqueous phase can proceed by two
ways: i) interfacial bimolecular electron transfer (ET) or ii) partition
of neutral Fc into the aqueous phase, followed by homogeneous electron transfer and subsequent ion transfer of Fc+ back from aqueous
to organic phase. In the first case, the current observed experimentally arises from the flux of electrons across the ITIES (bimolecular
ET mechanism), while in the latter case the observed current
comes from the transfer of Fc+ ions from water to oil (homogeneous
ET-IT mechanism).
Simulations were performed to evaluate which mechanism operates
at the interfacial electron transfer reaction at water-TFT interfaces. For
the case without a gold film, an heterogeneous bimolecular electron
transfer between Fc in TFT and [Fe(CN)6]3 − following the Butler–
Volmer kinetics was included in the model. Additionally, the ion transfer mechanism proposed by Osakai et al. [14], where Fc first partitions
into the aqueous phase to react homogeneously with Fe3+ and is transferred back across the ITIES as Fc+ was included. As calculated in
Eq. (12), the partition coefficient of Fc between TFT and water was estimated to be ca. 13,400. Both the bimolecular rate constant for the ET reaction and the homogeneous ET rate constants were varied in order to
reproduce experimental results from the cyclic voltammetry. Two
P. Peljo et al. / Journal of Electroanalytical Chemistry 779 (2016) 187–198
scans were simulated for comparison of the 2nd experimental scan.
Simulations of bimolecular ET mechanism alone in Fig. 1a and b clearly
show that this mechanism cannot satisfactory reproduce experimental
CVs. However, the simulations done considering only the partition of
ferrocene (Fig. 1c) followed by homogeneous electron transfer and
transfer of Fc+ ions across the interface show good agreement with
the experimental data. In this case, the homogeneous rate constant
was found to have a significant influence on the shape and peak current
magnitude of the simulated CVs. Fig. 1c shows that increasing
homogeneous rate constant increases the observed reversibility of
the signal. Unfortunately, the simulated data obtained with k1 =
1 × 109 s−1 M− 1 does not provide a satisfactory match between all
sets of the experimental data for different Fe(CN)3−/4–
concentrations
6
(Fig. 1d). This point will be discussed vide infra.
To successfully match the experimental voltammograms, the homogeneous rate constant had to be varied from 2 × 108 s− 1·M− 1 to
1 × 1010 s−1·M−1 to 5 × 109 s−1·M−1 for Fe2 +/3+ ratios of 10 mM/
100 mM, 55 mM/55 mM, and 100 mM/10 mM, in the aqueous phase, respectively (Fig. 2). Additionally, if both mechanisms are included in the
model, the contribution from the bimolecular ET mechanism is
Fig. 2. Effect of the homogeneous rate constant for different concentration of [Fe(CN)6]3−/4–.
(A) Experimental and (B) simulated cyclic voltammograms (IR compensated) of 0.1 mM Fc
and 5 mM BATB solution in TFT and [Fe(CN)6]3−/4– with various ratio between Fe2+ and
Fe3+ (Cells 1–3 in Scheme 1) at scan rate 10 mV/s. The homogeneous rate constant was
varied from 2 × 108 s−1·M−1 to 1 × 1010 s−1·M−1 to 5 × 109 s−1·M−1.
191
extremely small. Hence, this approach suggests that the electron transfer takes place almost solely by the partitioning of the ferrocene followed by homogeneous electron transfer in the aqueous phase and finally
by the transfer of ferrocenium into the organic phase, as suggested by
Osakai et al. [14].
The exact reproduction of experimental voltammograms is far from
simple, as many of the parameters are not accurately known. It has been
shown that iron hexacyano-complexes form ion pairs with cations [47,
48], inhibiting the ion transfer of potassium at the positive end of the
potential window. This effect as well as the effects of activities
were disregarded in the model, and the standard transfer potential
of potassium was tuned to 0.75 V to match the experimental
onset of the potassium transfer in all the three different ratios of
Fe 2 + /Fe 3 + resulting in different potassium concentrations.
Another difficulty is that the ferrocenium will slowly decompose
in the presence of water and oxygen [49–51]. Additionally, after
some experiments a blue-green precipitate was found to form at
the liquid–liquid interface, as reported earlier [52,53]. All these
factors contribute to the differences between experimental and
simulated voltammograms.
To further investigate this system, 100 mM LiCl was replaced with
10 mM Li2SO4 as a supporting electrolyte in Cells 4–7 to minimize the
complexation of iron with chloride, and different ratios of Fc to Fe3+
were tested at different scan rates, with the simulated and experimental
CVs shown in Fig. 3.
The slight shifts between some of the experimental results and
simulations may be due to the drifting of the Ag/AgCl reference electrode in the sulfate media during the experiments, in spite of the calibration of the Galvani potential scale with an internal standard after
the ET measurements. The voltammogram obtained with the scan
rate of 10 mV·s − 1 does not match the simulated CV. This may be
due to the change in the reaction mechanism: Aoki et al. reported
that at scan rates higher than ca. 20 mV·s− 1 the electron transfer reaction at thin film modified electrodes was taking place by penetration of the aqueous redox species into the organic film via selfemulsification, while at lower scan rates the ET reaction seemed to
be interfacial [43].
The formal potential of all these cases was also measured, with the
10/100 mM Fe2+/Fe3+ voltammogram showing the typical reversible
electron transfer on glassy carbon electrode. However, with lower concentrations of Fe3+, the electron transfer at glassy carbon electrode became very kinetically limited, with very wide peak-to-peak separations,
as shown in the Supplementary Material, Figure S-1. This observation
further justifies the strong variations of the electron transfer rate constants obtained by simulations. The homogeneous rate constants ranging from 2 × 107 s−1·M−1 (digital simulations of cyclic voltammetry
[14]) to 9 × 107 s− 1·M−1 (extrapolation of the measurements performed with micelles [54]) to 3 × 1010 s−1·M−1 (obtained from normal
pulse voltammetry [16]) have been reported in the literature. This large
variation reported in the literature and even within our own results reflects the complications with the ferri/ferrocyanide redox couple,
which, as it has been shown previously, shows strong ion pairing with
different cations [47,48].
Additionally, the self-exchange electron transfer rate with ferri/ferrocyanide has been shown to be significantly catalyzed by the presence of
various cations [55]. Also, the formal potential of the redox couple depends strongly on the supporting electrolyte and on the ionic strength.
In the present experiments, the ionic strength varied from 1 to 0.04 M. Indeed, if the logarithm of the obtained rate constant is plotted considering
pffiffi
pffiffi
the long-range Debye–Hückel interactions as the function of I=ð1 þ IÞ,
where I is the ionic strength, a linear correlation is obtained, as shown in
Fig. 4.
The rate constants determined by Tatsumi and Katano [15,16]
also fall on this line, while it seems that there is a outlier measurement at 10 mM/100 mM Fe 2 + /Fe 3 + ratio with 100 mM LiCl as a
supporting electrolyte. The value reported by Osakai et al. [14] is
192
P. Peljo et al. / Journal of Electroanalytical Chemistry 779 (2016) 187–198
Fig. 3. a–c) Experimental and simulated CVs obtained with Cells 4–6 in Scheme 1 (10/100 mM, 1/10 mM and 0.1/1 mM Fe2+/Fe3+). The simulated homogenous rate constants are
3 × 109 s−1·M−1 to 8 × 108 s−1·M−1 to 1 × 109 s−1·M−1. d) Simulated and experimental voltammograms obtained with Cells 5 and 7 in Scheme 1 (10/100 mM Fe2+/Fe3+ and 0.1
or 0.5 mM Fc).
also not on this line, and the reason for this discrepancy is currently
not known. One possible explanation might lie in the choice of the
cation: the data obtained in this work and by Tatsumi and Katano
Fig. 4. Correlation between logarithm of the rate constant and function F(I) considering
pffiffi
pffiffi
the long-range Debye–Hückel interactions. FðIÞ ¼ I =ð1 þ IÞ . Points on the graph
depict both data obtained in the current study and previously published values (refs.
[14,16]).
utilized potassium salts, while Osakai et al. used sodium ferro/ferricyanide. Indeed, the rate of reaction between for example persulfate and ferrocyanide depends strongly on both the type of the
cation and the ionic strength [56].
As the rate constants for the homogeneous reaction are very high,
the reaction layer thickness is extremely thin, varying from 10 to
100 nm depending on the initial concentrations and scan rate, as
shown in Figure S-2 in the Supplementary material. As the interface between two liquids is molecularly sharp but fluctuating within ca. 1 nm
thickness, (as predicted by molecular dynamics simulations [31] and
measured by neutron reflectivity [57]), the reaction layer is only slightly
thicker than the interface itself. Furthermore, double layer effects
should be considerable at these thicknesses.
The simulated CVs considering only heterogeneous ET had a different shape and too high magnitude in comparison with the experimental results. However, if the charge transfer coefficient α was
adjusted close to 0, the experimental voltammograms could be
reproduced. Osakai et al. reached the same conclusion (they wrote
the rate constants slightly differently, so they needed to adjust α
close to unity) [14]. The Marcus theory of the ET across the ITIES, predicts that α should be close to 0.5 [58] and thus does not support
these low values. Nevertheless, Samec has argued that this could be
due to the strong repulsion of negatively charged ferricyanide from
the electric double layer, due to the Frumkin effect [28]. Shao et al.
reported similar abnormally large transfer coefficients for the ET reactions at water/NPOE interface measured by SECM, and attributed
to the Frumkin effect on both sides of the interface [59].
P. Peljo et al. / Journal of Electroanalytical Chemistry 779 (2016) 187–198
193
Fig. 5. Effect of α on simulated CVs. a–b) The comparison between the experimental CVs and the simulations done with different α value for different amounts of total iron in aqueous
phase. c) Comparison of simulations with different α with 0.1 mM Fe2+ and 1 mM Fe3+ in the aqueous phase for different bimolecular interfacial electron transfer constants (c and d).
Scan rate 10 mV·s−1.
However, Osakai et al. could not fit all their experimental results
with the same parameters, so they concluded that “the interfacial
ET mechanism could not give a good explanation for the present system” [14]. Our results are very similar to the results of Osakai et al.
[14]. The effect of α is shown in Fig. 5. The differences between simulated and experimental values are more pronounced when the
amount of total iron in the aqueous phase is decreased to 1.1 mM
(0.1 mM [Fe(CN) 6] 4− + 1 mM [Fe(CN) 6] 3 −) while keeping the
ratio of Fe(II) and Fe(III) constant and the concentration of Fc in
the organic phase at 0.1 mM (Cell 6 in Scheme 1). In this case almost
no positive current was obtained at around 0.2 V, while the peak potential on the reverse scan was shifted by ca. 30 mV compared to the
experimental results.
However, the experimental data can be reproduced by changing the
value of k0 for the interfacial reaction, as shown in Fig. 6a). Detailed
analysis of the contribution of the different reactions to the total current
is shown in Figs. 6b) and c). At low Galvani potential differences the potential independent oxidation of Fc is balanced by the potential dependent reduction reaction, resulting in net zero current. Net current flow is
observed only when sufficiently high Galvani potential difference is applied to reduce the rate of the reduction of Fc, allowing the oxidation reaction to proceed. The rate of oxidation reaction then decreases due to
decreasing interfacial Fc concentration. After reversal of the scan direction the rate of the reduction reaction increases, and consequently, the
surface concentration of Fc and the oxidation current both increase
again. Additionally, the ion transfer of Fc+ has a small contribution to
the net current.
4.1.2. Mixed mechanisms
A third option to fit the experimental data would be the combination
of the interfacial heterogeneous electron transfer and homogeneous
electron transfer. In this case, the α value for the interfacial electron
transfer was fixed close to 0, with the standard electron transfer rate
constant (k0) fixed at 0.01 cm·s−1·M−1, and the homogeneous rate
constant (k1) was varied to reproduce the experimental voltammograms. In this case k1 could be ca. halved in comparison with the case
considering only homogeneous electron transfer, as shown in Fig. 7.
The most of the observed current results still from homogeneous reaction followed by ion transfer, but at higher Fe3+ concentrations the electron transfer mechanism starts to also play a more significant role, as
shown in Fig. 8. However, more accurate simulations considering also
the effect of the double layers would be required to clarify this issue.
The mixed mechanism can satisfactorily reproduce the experimental
data only if the αET is set close to zero. If αET would be set to 0.5, the peak
current on the forward sweep would be too high unless k0 would be set
to a very low value. In this case the situation would be as in Fig. 7a, so
that the all the reaction would take place by the ion transfer mechanism.
To reproduce the experimental data, both ion transfer mechanism and
interfacial electron transfer mechanism should show similar behavior,
and this is only achieved with αET close to 0.
4.1.3. Heterogeneous versus homogeneous electron transfer reactions at liquid–liquid interfaces: the wrong question?
In the introduction, we asked several questions concerning the electron transfer reactions observed at liquid–liquid interfaces, and in this
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P. Peljo et al. / Journal of Electroanalytical Chemistry 779 (2016) 187–198
drop occurs at the nm range [30], and we assume that all the parameters like electrochemical and chemical potentials of species, relative
permittivity, and density vary smoothly within this thin layer, we can
try give some estimations. We also need to consider the size and the orientation of the precursor b D | A N. The crystallographic radii of Fc and
[Fe(CN)6]3− are 0.33–0.365 nm [60,61] and 0.475 nm (computational
crystallographic radius, [62]), respectively, so the precursor spans over
this extremely thin interface. Another question is then, what is the closest approach for the different species to the interface. To observe the
current experimentally, the interface has to be polarized positively.
This would push negatively charged ions like [Fe(CN)6]3− from the interface further into the aqueous side. On the other hand, Fc can partition
into the aqueous phase, although with a high partition coefficient of ca.
13,400 favoring the TFT phase. This suggests that the reaction would
take place in the aqueous phase, without the precursor “feeling” almost
any potential drop. When the charge transfer has taken place, the positively charged D+ will move towards the interface while the negatively
charged A− will move further away, reducing the probability for the
back-reaction. In conclusion, the present data indicates that the precursor does not feel the potential drop.
ii). Where does the potential dependence of the observed current stem?.
Both reactions (2) and (3) can successfully reproduce the experimental
data. However, while the homogeneous rate constant increases with increasing ionic strength as shown in Fig. 5, the heterogeneous rate constant k0 decreases. As this decrease is difficult to justify theoretically,
only reaction (2) does not seem likely. Therefore, there are two possibilities: either the current originates from reaction (3) followed by transfer
Fig. 6. Effect of kET and contribution of IT and ET currents to the observed current.
a) Comparison of the experimental voltammograms obtained with Cells 4–6 and
simulated voltammograms obtained by varying the k0, with α set as 0. b) Contribution
of the interfacial oxidation and reduction of Fc and ion transfer of Fc+ on the total
current for low aqueous iron concentration (Cell 6) and c) for high aqueous iron
concentration (Cell 4). Scan rate 100 mV·s−1.
section we conclude what we learned from the present experiments
and simulations.
i). How much of the total interfacial potential drop does the
precursor b D | A N “feel” at the interface?. Unfortunately, this question
cannot be answered completely based on this work. However, if we
assume that the interface is molecularly sharp and the potential
Fig. 7. The comparison of the experimental and simulated voltammograms considering
only ion transfer mechanism a) or ion transfer mechanism and interfacial electron
transfer with very low αET value for forward reaction b). Scan rate 100 mV·s−1.
P. Peljo et al. / Journal of Electroanalytical Chemistry 779 (2016) 187–198
195
Fig. 9. Experimental and simulated cyclic voltammograms (IR compensated) with a gold
nanofilm deposited at the interface. 0.1 mM Fc and [Fe(CN)6]3−/4–with various ratio
between Fe2+ and Fe3+ were used. Scan rate 10 mV·s−1. Simulated CVs were obtained
considering a model where AuNP nanofilm acts as bipolar electrodes at the interface.
Fig. 8. The simulated contributions for the observed current from interfacial electron
transfer (ET) and from ion transfer across the interface (IT). The rate constant k1 was set
as in Fig. 7b, k0 = 0.01 cm·s−1·M−1 and αET = 0.01.
of D+, or the current is due to the sum of reactions (2) with α close to 0
and (3). As the current-potential response is similar from both reactions
(2) and (3), it is difficult to comprehensively answer this question with
only cyclic voltammetry, and more sensitive techniques are required to
answer these questions.
In case of the heterogeneous electron transfer scenario, if α = 0, it
means that the rate of oxidation of ferrocene does not directly depend
on the applied Galvani potential difference, but instead the reaction
rate is dependent on the interfacial concentrations. However, the back
reduction rate still depends on the applied potential, as shown in
Fig. 7 b) and c). The oxidation can only take place when sufficient
Galvani potential difference is applied to significantly reduce the rate
of the reduction, otherwise both reactions are in equilibrium and the
net current flow is zero. In fact, there is a striking similarity with the heterogeneous electron transfer mechanism with α = 0 and with the homogeneous pre-partitioning mechanism. In both cases, the rate of the
ferrocene oxidation does not directly depend on the potential, but is
limited by another potential dependent reaction: in the case of the ET
mechanism the reaction is the heterogeneous reduction, while in the
case of the pre-partitioning mechanism the limiting reaction is the ion
transfer of ferrocenium back to the organic phase. If the ferrocenium
cannot transfer into the organic phase, the homogeneous reaction
reaches equilibrium and does not proceed anymore. Hence, it is not surprising that both mechanisms can successfully reproduce the experimental data. This was actually pointed out by Senda et al. [18].
In conclusion, it appears that in the pre-partitioning mechanism the
observed potential dependence stems from that of the concomitant ion
transfer reactions. This may also explain some earlier observations of
the potential independent interfacial electron transfer: if the reactions
are studied in the potential range where the concomitant ion transfer
reaction is very slow, there will be almost no potential dependence.
Finally, the question about the homogeneous or heterogeneous reaction is perhaps not the most important one. This work shows that a
more relevant question is: Can the electron transfer reaction be considered as independent of the applied potential? The answer being most
likely: Yes.
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P. Peljo et al. / Journal of Electroanalytical Chemistry 779 (2016) 187–198
4.1.4. Redox catalysis by a gold nanofilm
In the presence of a gold film at the interface formed by adsorption of
gold nanoparticles, a model treating the gold film as a bipolar metallic
thin film electrode with separate Butler–Volmer kinetics for both Fc+/
Fc and Fe2 +/Fe3 + was also employed. The rate constant of
0.04 cm·s−1 on gold electrode in accordance with work of Samec
et al. [47] was used for the hexacyanoferrate, and the rate constant of
ferrocenium/ferrocene reaction (k0o) was varied to obtain satisfactory
similarity with the experimental voltammograms (Fig. 9), resulting in
rate constants of 0.1–0.01 cm·s−1.
Comparison of experimental and simulated CVs shows that the CV
obtained with the Fe2+/Fe3+ ratio of 10/100 has lower current, but otherwise the match is very good. The CVs show that the electron transfer
reactions are limited by the mass transport of Fc/Fc+, so it is difficult to
compare different plausible mechanisms. In fact, the model results were
almost identical with the simulated voltammetry of ferrocene obtained
on a solid electrode. In the simulations, the Galvani potential difference
was set between the organic and the aqueous phase, while the potential
drop in the metal film in the middle was calculated from Ohms law (and
being negligible). So in practice the film could be considered equipotential. A bipolar model allows separation of the overpotentials required to
drive both reactions. In this case, the amount of Fe3 + in the aqueous
phase was so high that practically all the overpotential was on the organic side.
One could also argue that the gold nanofilm catalyzes strongly the
heterogeneous interfacial electron transfer between Fc and Fe3+, but
in this case rate constants of 0.1 to 1 cm·s−1·M−1 would be required
to obtain reversible CVs. Hence, the bipolar electrode model is more
likely, and this model is supported by the observation of nanofilm catalyzed interfacial oxygen reduction by DMFc in the organic phase. These
numerical simulations collaborate the simplified models for interfacial
redox catalysis presented in ref. [35].
Another interesting question is, how the Galvani potential difference
is distributed across the interface covered with the gold nanofilm.
At the metal-solution interface, a redox equilibrium gives [63,64]
h
i
aox
0;S
M
F ϕM −ϕS ¼ μ ox
þ
RT
ln
−μ 0;S
þ
μ
–
e
red
ared
ð15Þ
where μeM– is the chemical contribution to the electrochemical potential
of the electron that can be expressed as
M
M
μM
e– ¼ α e– þ Fχ ¼ −Φe– þ Fχ
So for the 55 mM/55 mM ferri-ferro cyanide side, we have
ϕM −ϕw ¼ 0:467 V þ 4:44 V−5:30 V þ χ ¼ −0:393 V þ χ
ð20Þ
ϕM −ϕo ¼ 0:736 V þ 4:44 V−5:30 V þ χ ¼ −0:124 V þ χ
ð21Þ
as illustrated in Scheme 2 considering that χ = 0.
The half-wave Galvani potential difference for the electron transfer
reaction then becomes
ϕw −ϕo ¼ − Eox=red w −ΦM
Eox=red o −ΦM
e– =F þ χ þ
e– =F þ χ ¼
¼ Eox=red o − Eox=red w ¼ 0:269 V
ð22Þ
as can be seen in Figs. 5c–d and 9. This is actually the same expression as
can be derived considering the thermodynamic equilibrium of Eq. (4)
[2,3]. Herein the value of [EFc+/Fc]o was tuned from 0.72 V to 0.736 V to
reproduce the experimental voltammograms in Fig. 9.
In any case, the gold nanofilm acts as an array of microelectrode with
an overlapping diffusion fields thereby preventing the partition of the
ferrocene in the aqueous phase. As the gold film is in pre-equilibrium
with the aqueous redox couple, this half-wave potential for this mediated ET reactions corresponds to Eq. (22). In this pre-equilibrium situation, the Fermi level of the electrons in water and in the gold NPs are
equal.
The major difference between Figs. 1 and 9 stems from both the reaction kinetics and mass transfer. In Fig. 1 the ET reaction in water is kinetically limited whereas the ion transfer reactions are mass transfer
controlled. In Fig. 9 the mass transfer of the organic redox couple limits
the ET reaction at the gold nanofilm.
5. Conclusions
The electron transfer between ferrocene dissolved in the organic
phase, and ferri/ferrocyanide dissolved in the aqueous phase was studied by cyclic voltammetry and by finite element simulations. These results indicate that electron transfer between slightly partitioning
neutral species in the organic phase takes place by the so-called prepartition mechanism, where ferrocene firstly partitions into the aqueous phase to react homogeneously with Fe3+ species. The observed current results from the transfer of ferrocenium cation back from aqueous
to oil phase. The rate constant of the homogeneous electron transfer reaction in the aqueous phase was found to be strongly dependent on the
ð16Þ
where αeM– is the real potential of electrons in metal (the work to bring
an electron from vacuum into the metal),χ is the surface potential of
polycrystalline gold in solution and ΦeM– is the work function of gold.
By definition, αeM– = μeM– − Fχ and αeM– = −ΦeM– [63,64].
Also, the Nernst equation is
h
i
aox
0;w 1 0
0;S
þ
RT
ln
−μ 0;S
−
μ
F Eox=red S ¼ μ ox
þ − μH
red
H
2 2
ared
ð17Þ
with
1
− μ 0H2 =F ¼ 4:44 V
μ 0;w
Hþ
2
ð18Þ
Then, the Galvani potential difference is given by
1 0
ϕM −ϕS ¼ Eox=red S þ μ 0;w
=F−ΦM
þ − μH
e– =F þ χ
2
H
2
¼ Eox=red S þ 4:44−5:30 þ χ
ð19Þ
Scheme 2. Potential profile with gold nanofilm covered interface at the half-wave
potential of electron transfer reaction with Cell 2, considering that χ = 0. The Fermi
levels of electrons in all phases are equal at this applied Galvani potential difference.
P. Peljo et al. / Journal of Electroanalytical Chemistry 779 (2016) 187–198
ionic strength of the aqueous phase, varying from 8 × 108 s−1·M−1 to
pffiffi
1 × 1010 s−1·M−1, with a linear correlation between log k and I=ð1 þ
pffiffi
I Þ. Accurate measurements are complicated by the side reactions of
ferrocenium, and in some cases by precipitation of Prussian Blue type
salts. When a gold nanofilm was added to the liquid–liquid interface,
the electron transfer mechanism changed to bipolar mechanism,
where the nanofilm acts as a bipolar electrode, shuttling the electrons
between the redox couples in different phases and drastically increasing
the electron transfer rate.
However, our results cannot completely rule out the interfacial electron transfer mechanism where α is close to 0 due to the Frumkin effects, or the mixed mechanism where both interfacial electron transfer
mechanism with α close to 0 and the pre-partitioning mechanism operate in tandem. It is not surprising that all the three mechanisms can accurately reproduce the experimental data, as both cases a potential
independent step is coupled with a potential dependent reaction (reduction of Fc+ in the case of interfacial electron transfer mechanism
whit α close to 0, and ion transfer of Fc+ in the case of the prepartitioning mechanism).
To conclude, the question about the homogeneous or heterogeneous
reaction is perhaps not the most important one. This work shows that a
more relevant question is: Can the electron transfer reaction be considered as independent of the applied potential? The answer being most
likely: Yes.
Acknowledgments
We would like to acknowledge financial support from Swiss National Science Foundation (Grant: Solar Fuels 2000-20_152 557/1),
Fondazione Oronzio e Niccoló De Nora, and EPFL.
Appendix A. Supplementary data
Supplementary data to this article containing the details of the finite
element simulations, voltammetry of Fe(II)/Fe(III) in aqueous solution
and the simulations of the reaction layer thicknesses in the aqueous
phase can be found online at http://dx.doi.org/10.1016/j.jelechem.
2016.02.023.
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